In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit-evasion ...

We present a new speedup technique for route planning that exploits the hierarchy inherent in real world road networks. Our algorithm preprocesses the eight digit number of nodes needed for maps of the USA or Western Europe in a few hours using linear space. Shortest (i.e. fastest) path queries then take around eight milliseconds to produce exact shortest paths. This is about 2 000 times faster...

We address robust path planning for a mobile agent in a general environment by nding minimum cost source-destination paths having prescribed widths. The main result is a new approach which optimally solves the robust path planning problem using an e cient network ow formulation. Our algorithm represents a signi cant departure from conventional shortest-path or graph search based methods; it not...

In this paper, Self-Organizing Map (SOM) for the Multiple Traveling Salesman Problem (MTSP) with minmax objective is applied to the robotic problem of multigoal path planning in the polygonal domain. The main difficulty of such SOM deployment is determination of collision-free paths among obstacles that is required to evaluate the neuron-city distances in the winner selection phase of unsupervi...

We study the complexity of two Inverse Shortest Paths (ISP) problems with integer arc lengths and the requirement for uniquely determined shortest paths. Given a collection of paths in a directed graph, the task is to find positive integer arc lengths such that the given paths are uniquely determined shortest paths between their respective terminals. The first problem seeks for arc lengths that...

In this paper a novel method is presented for robot motion planning with respect to two objectives, the shortest and smoothest path criteria. A Particle Swarm Optimization (PSO) algorithm is employed for global path planning, while the Probabilistic Roadmap method (PRM) is used for obstacle avoidance (local planning). The two objective functions are incorporated in the PSO equations in which th...

We address robust path planning for a mobile agent in a general environment by finding minimum cost source-destination paths having prescribed widths. The main result is a new approach that optimally solves the robust path planning problem using an efficient network flow formulation. Our algorithm represents a significant departure from conventional shortest-path or graph search based methods; ...

We describe a novel global path planning method for autonomous qualitative navigation in indoor environments. Global path planning operates on top of a qualitative map of the environment that describes variations in sensor behavior between adjacent regions in space. The method takes into consideration the global topology of the environment and applies a set of criteria that can minimize the err...